Air carrier Captain reported receiving a terrain alert while maneuvering on a RNAV RNP approach in mountainous terrain. The crew incorrectly set the minimum altitude on a crossing fix during the initial approach in visual conditions; which triggered the GPWS alert; the crew corrected the vertical profile; and landed.

Narrative

While flying the RNAV (RNP) Y 17L approach into RNO; we received a GPWS warning . I continued the approach to landing because the First Officer (FO) and I 1) had visual site of the terrain; which created no hazard; 2) I had already begun to arrest the descent rate when the GPWS warning occurred; and we were stabilized. I received a call from FOQA personnel the following morning with whom I discussed the circumstances leading to the GPWS warning and possible options to consider if faced with a similar event. We were high on the approach due to not being cleared for the approach until after we crossed the IF (KLOCK). In order to recapture the approach path I selected LVL CHANGE; began configuring the aircraft and set the altitude to 6400; the altitude for the next point WORTH. Just outside of WORTH we recaptured the approach path. I believe I selected VNAV; but either it didn't activate or I failed to select it at all. Either way the aircraft remained in LVL CHANGE as I set minimums of 4800 and transitioned to visual landing with the airport at about the 10 o'clock position. At approximately 5500 ft and just outside URATE I acquired the PAPI lights and noticed we were slightly low (3 red/1 white). At the same time we received a TERRAIN warning from GPWS. I disconnected the Autopilot and began to pitch up for 2 red/2 white on the PAPI. At that moment we received a WHOOP WHOOP PULL UP alert associated the hill next to URATE; which the FO and I had visual sight of passing off our left and behind us. No further alerts we received and with the initial pitch to level flight we were on PAPI glidepath (2 red/2 white); so I elected to continue the approach to landing. The next morning I played the animation of the landing to determine what led to the GPWS warning. After several viewings I realized the aircraft remained in LVL CHANGE; not VNAV like I believed was happening at the time; with a higher rate of descent than normal. The higher rate of descent triggered the GPWS. About an hour later FOQA personnel called and we discussed the event in detail. Cause: Late clearance for the approach. Failure to recognize aircraft automation did not transition from LVL CHANGE to VNAV.